Calculate the mean-variance-standard deviation

Question

Question: Consider the following Table:

Y       0         1          2         3

P(Y) 0.10   0.30     0.40

(a) Complete the Table with the probability of P(X = 3).

(b) Calculate the mean, variance and standard deviation of Y.

(c) Suppose now we have a new random variable X = 2 + 3Y. Construct a 'Bible with the probability distribution of X for each value of Y and X.

(d) Calculate the mean, variance and standard deviation of X.

(e) Use the properties of the expected value and variance to obtain the ex­pected value of X, E(X), and the variance of X, V(X). Compare your answers.